insufficient pull down current at lower level voltages.
I would use a set of transistors and switch them off and on, that way current is more controllable. Can even go into using op-amps as comparators so when the battery hits a certain voltage it will switch to a different transistor set up for lower voltages, and at the coupling node to the input use two diodes to keep the other higher voltage transitor from leaking current. For sure the first transistor would be a common emitter NPN and the second might be a transistor and/or low power fet that needs a low to turn on.
It is up to you, but I figure being able to set the state of the circuit more actively would yield a better response.
At what voltage does this start to happen??
Just a thought:
BEC, or battery elimination circuitry is incorporated into most small signal receivers in cooperation from a ESC Electronic speed control, which would work in a way so that even if the battery has dumped the receiver still has enough power to run servos without an external receiver battery and cut the power going to the main motor. This circuitry switches states as the battery gets more discharged.